‘The Book of Mormon” isn’t the only show in town to poke fun of Mitt Romney’s faith. Enter “Missionary in Manhattan” which is pretty amusing, if a lot less profane — and just $15 a ticket.

Presented by the “Ukulele Orchestra of Great Brooklyn,” this tidy little musical features a homespun-dressed trio of polygamist pop stars — Sister Gretchen (Caitlin Davis), Sister Bunny Katherine (Elizabeth May, who co-wrote the show with Davis) and Sister Fanny (Lily Narbonne) — strumming away on their little instruments.

These merry sister wives have embarked on a “Have You Seen Him Tour” in search of their missing husband, Charles. He was last seen, suspiciously enough, at Manhattan’s Cubby Hole, in the company of his male vocal coach.

Between appeals to the audience, they sweetly warble Church of the Latter-day Saint versions of pop hits like the Weather Girls’ “It’s Raining Men” (“It’s Raining Mormons”), Rihanna’s “Only Girl (In the World)” (“She’s a good role model for us,” they proclaim) and Cee Lo Green’s “Forget You,” or in this case, “Bless You.”

They also turn their ukuleles into puppets for a story-theater style re-creation of Joseph Smith’s visitation from an angel that inspired his Book of Mormon.

Though they get little help from the audience — “Y’all look a little bit Jewish,” a Mormon wife points out — they eventually find their wayward hubby (Dave May), fresh from his sojourn to Fire Island.

Clocking in at just 45 minutes, “Missionary in Manhattan” is little more than an extended musical sketch. But it’s an amusing one, and the deadpan performances and Kaleigh Malloy’s lighthearted staging add to the fun.

Let’s face it: It’s hard to be unhappy when you’re surrounded by ukuleles.